simplify 12^{3/2}

Solution

simplify

1 2^{\frac{3}{2}}

24 \cdot 3^{\frac{1}{2}}

Solution steps

1 2^{\frac{3}{2}}

Prime factorization of

12 : 2^{2} \cdot 3

= (2^{2} \cdot 3)^{\frac{3}{2}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(2^{2} \cdot 3)^{\frac{3}{2}} = (2^{2})^{\frac{3}{2}} \cdot 3^{\frac{3}{2}}

= (2^{2})^{\frac{3}{2}} \cdot 3^{\frac{3}{2}}

(2^{2})^{\frac{3}{2}} = 8

= 8 \cdot 3^{\frac{3}{2}}

3^{\frac{3}{2}} = 3 \cdot 3^{\frac{1}{2}}

= 8 \cdot 3 \cdot 3^{\frac{1}{2}}

Multiply the numbers:

8 \cdot 3 = 24

= 24 \cdot 3^{\frac{1}{2}}

- (- 2 x + 1) = 9 - 14 x

(x^{\frac{1}{3}})^{\frac{1}{2}}

x^{2} + x + 53 = 4 - 13 x

y^{2} + y - 20

(1)^{\frac{1}{2}}